Download - I) Measurement of Resistance
Electrical Measurements
Measurement of Resistances;
Potentiometers;
AC Bridge Methods for Measurement of Inductance &
Capacitance;
Magnetic Measurements
Measurement of Resistances
1. Low Resistance: Up to 1Ω;2. Medium Resistance: 1Ω to 100KΩ;3. High Resistance: Above 100KΩ.
Measurement of Medium Resistances:
1. Ammeter-Voltmeter Method;2. Substitute Method;3. Wheatstone Bridge Method;4. Ohmmeter Method.
aaR
m RRI
VVIVR +=
+==1
V
VRm
RR
RII
VR+
=+
=1
2
−=
11 1
m
am R
RRR
−=
V
mm
RRRR
22
1
1
1. Ammeter-Voltmeter Method:
2. Substitution Method:
Accuracy of this method is greatly affected if there is any change inthe battery emf.
This method is not widely used for medium resistancemeasurements and is used in a modified form for measurement ofhigh resistances.
3. Wheatstone Bridge Method:
SR
QP=
RIPI 21 =
QPEII+
== 31
SREII+
== 42
Sensitivity of Bridge
QPEPPIEab +
== 1 ( ) ( )( )SRR
RRERRIEad +∆+∆+
=∆+= 2
+
−+∆+
∆+=−=
QPP
SRRRREEEe abad SR
RQP
P+
=+
( ) ( )SRRSRRESe
+∆++∆
= 2 ( )2SRRESe
+∆
=
SV be the voltage sensitivity of Galvanometer ( )2SR
RESSeS VV +∆
==θ
SB is the Bridge Sensitivity
RRSB ∆
=θ
RS
SR
ESS VB
++=
2 4ESS V
B =
4. Ohmmeter Method:(i) Series Type Ohmmeter:
RX = Unknown Resistance;Rm = Internal Resistance of the meter;Rh = Half scale position Resistance;Ih = Half-full scale deflection;Ifm = Full scale deflection current of the meter;If = Full scale deflection battery current
msh
mshseh RR
RRRR+
+=
hh R
VI2
=h
hf RVII == 2
fmfsh III −= mfmshsh RIRI =
hfm
hmfm
fmf
mfmsh RIV
RRIII
RIR
−=
−=
VRRI
RRR
RRRR hmfmh
msh
mshhse −=
+−=
(ii) Shunt Type Ohmmeter:
RX = Unknown Resistance;Rm = Internal Resistance of the meter;Rh = Half scale position Resistance;IB = Battery Current;Ifm = Full scale deflection current of the meter;If = Full scale deflection battery current
msefm RR
VI+
=
Xm
Xmse
B
RRRRR
VI
++
=
Xm
X
Xm
Xmse
m RRR
RRRRR
VI+
++
= .
( )( ) XmXmse
mseX
fm
m
RRRRRRRR
IIS
+++
==
PX
X
RRRS+
=
(iii) Crossed Coil Type Ohmmeter:
(a) Fixed Magnetic Moving Coil (b) Crossed Coil Moving Magnetic
Measurement of Low Resistances:
Measured Resistance
Contact Resistance % error
100Ω0.002Ω
Negligible
0.02Ω 10%
Methods for Measurement of Low Resistance
1. Ammeter-Voltmeter Method;
2. Kelvin Double Bridge Method;
3. Potentiometer Method.
Kelvin Double Bridge Method:
QP
rr=
2
1
QPP
rrr
+=
+ 21
1
rQP
Pr+
=1 rQP
Qr+
=2
+
+=
+
+ rQP
QSQPr
QPPR
SR
QP=
acab EQP
PE+
=
++
+++=
rqprqpSRIEac
)(
+++
++=
rqprqp
qppRIEamd
)(
++
+=rqp
prRIEamd
++
+=
+++
+++ rqp
prRIrqprqpSRI
QPP )(
−
+++=
qp
QP
rqpqrS
QPR
SR
QP=
Measurement of High Resistances:
1. Insulation resistance of cables;
2. Resistance of high resistance circuit elements;
3. Volume resistivity of a material;
4. Surface resistivity.
Difficulties in Measurement of High Resistances
1. Due to leakage current;
2. Due to electrostatic effect;
3. Definite ratios in potential distribution with respect to
surroundings;
Use Guard Circuit
Methods for Measurement of High Resistance:
1. Price’s Guard-wire Method;2. Loss of Charge Method;3. Megohm Bridge Method;4. Megger Method.
Price’s Guard Wire Method:
Measurement of Volume and Surface Resistivity
d1 = Diameter of the upper electrode d1;d2 = Diameter of the lower electrode d2;t = Thickness of the specimen sheet;V1 , V2 = Reading of voltmeter;I1 = current through galvanometer G1 ;I2 = current through galvanometer G2
Volume resistivity of specimen:
1
12
12
1
44 IV
tdR
td ππρ ==
Surface Resistivity:
2
222
2
IV
tdR
td
sππρ ==
Loss of Charge Method:
dtdvC
dtdqi −=−=
Again,'R'
R' across drop PotentialRVi ==
dtdvC
RV
−=' 'CR
dtVdv
−=
∫ ∫−=2
1 0 '
V
V
t
CRdt
Vdv
'12
CRt
eVV −=
''
1
1
RRRRR−
=
Megohm Bridge Method:
Megger Method:
Detail Circuit Diagram: